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A272680 Smallest square that begins with n (in binary).

%I A272680 #16 May 23 2016 08:06:11
%S A272680 0,1,4,25,4,81,25,121,16,9,81,361,25,441,225,121,16,1089,36,625,81,
%T A272680 169,361,1521,49,25,841,441,225,3721,121,2025,64,529,1089,4489,36,
%U A272680 2401,1225,625,81,5329,169,2809,11449,361,5929,1521,6241,49,100,6561,841,6889
%N A272680 Smallest square that begins with n (in binary).
%D A272680 Allan C. Wechsler, posting to math-fun mailing list May 22 2016.
%H A272680 Chai Wah Wu, <a href="/A272680/b272680.txt">Table of n, a(n) for n = 0..10000</a>
%e A272680 a(10)=81, because 81 = 9^2 = 1010001_2 begins with 1010 = 10_2.
%o A272680 (Python)
%o A272680 from gmpy2 import isqrt
%o A272680 def A272680(n):
%o A272680     if n == 0:
%o A272680         return 0
%o A272680     else:
%o A272680         d, nd = 1, n
%o A272680         while True:
%o A272680             x = (isqrt(nd-1)+1)**2
%o A272680             if x < nd+d:
%o A272680                 return int(x)
%o A272680             d *= 2
%o A272680             nd *= 2 # _Chai Wah Wu_, May 22 2016
%Y A272680 Cf. A007088, A018851, A018796, A272679, A272681.
%K A272680 nonn,base,easy
%O A272680 0,3
%A A272680 _N. J. A. Sloane_, May 22 2016
%E A272680 More terms from _Chai Wah Wu_, May 22 2016